Compute, display and comment the sample correlation matrix.
Display jointplots for each pair of variables.
Perform PCA on covariates
Pairwise analysis did not provide us with a clear and simple picture of the French-speaking districts.
Play with centering and scaling
Project the dataset on the first two principal components (perform dimension reduction) and build a scatterplot. Colour the points according to the value of original covariates.
Sanity checks
\(X\) : data matrix after column centering (use scale(., center=T, scale-F))
\[X\]
Checking Orthogonality of \(V\)
Compare standardized and non-standardized PCA
Pay attention to the correlation circles.
How well are variables represented?
Which variables contribute to the first axis?
Explain the contrast between the two correlation circles.
In the sequel we focus on standardized PCA.
Investigate eigenvalues of covariance matrix
How many axes should we keep?
Provide an interpretation of the first two principal axes
Which variables contribute to the two first principal axes?
Analyze the signs of correlations between variables and axes?
Add the Fertility variable
Plot again the correlation circle using the same principal axes as before, but add the Fertility variable. How does Fertility relate with covariates? with principal axes?